Solutions Manual For Finite Mathematics 7th Edition By
Stefan Waner; Steven Costenoble
Conjecture - ANSWER: The conclusion formed by using inductive reasoning, since it
may or may not be correct.
Inductive reasoning - ANSWER: Is the process of reaching a general conclusion by
examining specific examples.
Example of inductive reasoning - ANSWER: When you examine a list of numbers and
predict the next number in the list according to some pattern, you are using
inductive reasoning.
Counterexample - ANSWER: If you can find one case for which a statement is not
true, then the statement is a false statement.
Deductive reasoning - ANSWER: Is the process of reaching a conclusion by applying
general assumptions, procedures, or principles.
Example of deductive reasoning - ANSWER: Solving logic puzzles.
Sequence - ANSWER: An ordered list of numbers such as 5, 14, 27, 44, 65,...
Terms - ANSWER: The numbers in a sequence that are separated by commas.
nth term of a sequence - ANSWER: It is customary to use the subscript notation an
for the nth term. That is a₁ represents the first term of a sequence. a₂ represents the
second term of a sequence. a₃ represents the third term of a sequence...an
represents the nth term.
Difference table - ANSWER: Shows the differences between successive terms of the
sequence.
First differences - ANSWER: Are in row 1. Are the differences of the terms (numbers).
Second differences - ANSWER: Are are in row 2. Are the differences of the first
differences.
Third differences - ANSWER: Are in row 3. Are the differences of the second
differences.
nth term formula for a sequence - ANSWER: Used to predict next term of a
sequence. In some cases we can use patterns to predict a formula.
Fibonacci sequence - ANSWER: The unending sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, ...
where each term is defined as the sum of its two predecessors.
, Recursive definition for a sequence - ANSWER: Is one in which each successive term
of the sequence is defined by using some of the preceding terms.
The Fibonacci numbers - ANSWER: If we use the mathematical notation Fn to
represent the nth Fibonacci number, then the numbers in the Fibonacci sequence
are given by the following recursive definition. F₁=1, F₂=1, and Fn=Fn-1+Fn-2 for n≥3.
Polya's four-step problem-solving strategy - ANSWER: 1. Understand the problem. 2.
Devise a plan. 3. Carry out the plan. 4. Review the solution.
Set - ANSWER: Any group or collection of objects.
Elements or members - ANSWER: The objects that belong in a set.
One method used to designate a set - ANSWER: Describe the set using words.
Roster method - ANSWER: Another method used to designate a set. List the
elements of the set inside a pair of braces. [ ]. Commas are used to separate the
elements.
Real numbers - ANSWER: R=the set of all rational or irrational numbers.
Natural or counting numbers - ANSWER: N={1,2,3,4,5,...}
Whole numbers - ANSWER: W={0,1,2,3,4,5...}
Integers - ANSWER: I={...,-3,-2,-1,0,1,2,3,...}
Rational numbers - ANSWER: Q=the set of all terminating or repeating decimals.
1/2=.5, 1/4=.25, 1/3=.3
Irrational numbers - ANSWER: i=the set of all nonterminating, non-repeating
decimals. √2, π, e.
empty or null set - ANSWER: ∅
... - ANSWER: ellipse
Negative integers - ANSWER: ...,-4,-3,-2,-1
Positive integers - ANSWER: 1,2,3,4,...
When a set is well defined - ANSWER: If it is possible to determine whether any given
item is an element of the set.
Stefan Waner; Steven Costenoble
Conjecture - ANSWER: The conclusion formed by using inductive reasoning, since it
may or may not be correct.
Inductive reasoning - ANSWER: Is the process of reaching a general conclusion by
examining specific examples.
Example of inductive reasoning - ANSWER: When you examine a list of numbers and
predict the next number in the list according to some pattern, you are using
inductive reasoning.
Counterexample - ANSWER: If you can find one case for which a statement is not
true, then the statement is a false statement.
Deductive reasoning - ANSWER: Is the process of reaching a conclusion by applying
general assumptions, procedures, or principles.
Example of deductive reasoning - ANSWER: Solving logic puzzles.
Sequence - ANSWER: An ordered list of numbers such as 5, 14, 27, 44, 65,...
Terms - ANSWER: The numbers in a sequence that are separated by commas.
nth term of a sequence - ANSWER: It is customary to use the subscript notation an
for the nth term. That is a₁ represents the first term of a sequence. a₂ represents the
second term of a sequence. a₃ represents the third term of a sequence...an
represents the nth term.
Difference table - ANSWER: Shows the differences between successive terms of the
sequence.
First differences - ANSWER: Are in row 1. Are the differences of the terms (numbers).
Second differences - ANSWER: Are are in row 2. Are the differences of the first
differences.
Third differences - ANSWER: Are in row 3. Are the differences of the second
differences.
nth term formula for a sequence - ANSWER: Used to predict next term of a
sequence. In some cases we can use patterns to predict a formula.
Fibonacci sequence - ANSWER: The unending sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, ...
where each term is defined as the sum of its two predecessors.
, Recursive definition for a sequence - ANSWER: Is one in which each successive term
of the sequence is defined by using some of the preceding terms.
The Fibonacci numbers - ANSWER: If we use the mathematical notation Fn to
represent the nth Fibonacci number, then the numbers in the Fibonacci sequence
are given by the following recursive definition. F₁=1, F₂=1, and Fn=Fn-1+Fn-2 for n≥3.
Polya's four-step problem-solving strategy - ANSWER: 1. Understand the problem. 2.
Devise a plan. 3. Carry out the plan. 4. Review the solution.
Set - ANSWER: Any group or collection of objects.
Elements or members - ANSWER: The objects that belong in a set.
One method used to designate a set - ANSWER: Describe the set using words.
Roster method - ANSWER: Another method used to designate a set. List the
elements of the set inside a pair of braces. [ ]. Commas are used to separate the
elements.
Real numbers - ANSWER: R=the set of all rational or irrational numbers.
Natural or counting numbers - ANSWER: N={1,2,3,4,5,...}
Whole numbers - ANSWER: W={0,1,2,3,4,5...}
Integers - ANSWER: I={...,-3,-2,-1,0,1,2,3,...}
Rational numbers - ANSWER: Q=the set of all terminating or repeating decimals.
1/2=.5, 1/4=.25, 1/3=.3
Irrational numbers - ANSWER: i=the set of all nonterminating, non-repeating
decimals. √2, π, e.
empty or null set - ANSWER: ∅
... - ANSWER: ellipse
Negative integers - ANSWER: ...,-4,-3,-2,-1
Positive integers - ANSWER: 1,2,3,4,...
When a set is well defined - ANSWER: If it is possible to determine whether any given
item is an element of the set.
